Numerical Implementation of the Contact of Optimal Trajectory with Singular Regime in the Optimal Control Problem with Quadratic Criteria and Scalar Control

  • Alexander P. Afanas’evEmail author
  • Sergei M. Dzyuba
  • Irina I. Emelyanova
  • Elena V. Putilina
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)


Previous works by these authors offer the numerical method of successive approximations for developing the solutions of the problem of stabilization of nonlinear systems with standard functional. This paper considers applying this method for studying the problem with singular control. It is achieved by introducing an auxiliary problem. The solution for the auxiliary problem provides a smooth approximation to the solution of the initial problem. The paper presents the algorithms for constructing an approximate solution for the initial problem. It is demonstrated that unlike direct algorithms of optimal control, these algorithms allow registering the saturation point, thus enabling one to register and study singular regimes.


Method of successive approximations Problem of minimizing a quadratic functional for a class of nonlinear systems with scalar control Singular control 



This research was supported by the Russian Science Foundation, grant no. 16-11-10352.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexander P. Afanas’ev
    • 1
    • 2
    • 3
    Email author
  • Sergei M. Dzyuba
    • 4
  • Irina I. Emelyanova
    • 1
    • 2
    • 3
    • 4
  • Elena V. Putilina
    • 1
  1. 1.Institute for Information Transmission Problems RASMoscowRussia
  2. 2.National Research University Higher School of EconomicsMoscowRussia
  3. 3.Lomonosov Moscow State UniversityMoscowRussia
  4. 4.Tver State Technical UniversityTverRussia

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